Cofinal types of ultrafilters

被引：21

作者：

Raghavan, Dilip ^{[1
]}

Todorcevic, Stevo ^{[2
]}

机构：

[1] Kobe Univ, Grad Sch Syst Informat, Nada Ku, Kobe, Hyogo 6578501, Japan

[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2012年 / 163卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Cofinal type; Ultrafilter; Tukey reducibility; Rudin-Keisler order; CATEGORY;

D O I：

10.1016/j.apal.2011.08.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study Tukey types of ultrafilters on omega, focusing on the question of when Tukey reducibility is equivalent to Rudin-Keisler reducibility. We give several conditions under which this equivalence holds. We show that there are only c many ultrafilters that are Tukey below any basically generated ultrafilter. The class of basically generated ultrafilters includes all known ultrafilters that are not Tukey above vertical bar omega(1)vertical bar(<omega). We give a complete characterization of all ultrafilters that are Tukey below a selective. A counterexample showing that Tukey reducibility and RK reducibility can diverge within the class of P-points is also given. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：185 / 199

页数：15

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